An input-output view of robustness in adaptive control

The stability and robustness properties of adaptive control systems are examined using input-output stability theory, i.e. passivity and small-gain theory. A generic adaptive error system is developed based on the concept of a tuned system—an ideal converged (nonadaptive) closed-loop system. Using this error system with passivity theory gives conditions for global stability where only boundedness (in norm) is required on the external inputs, e.g. disturbance, reference and initial conditions. Small gain theory is used to develop local stability results where the magnitudes of the external inputs are restricted. In the global case, a particular system operator (not the plant) is required to be strictly-passive, a condition which is unlikely to hold in actual use due to unmodeled dynamics. The local results, however, are not so restricted and allow for unmodeled dynamics. In this latter case an estimate of the stability margin is given under a persistent excitation condition.